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DUFFY_Ch02.qxd 3/4/07 6:09 PM Page 29 The Evolution of Stephen M. Crustacean Mating Shuster Systems The alpha males of the isopod Paracerceis sculpta allow reproductive females (here inside the sponge) to enter their host sponges; beta males and tiny gamma males, which are morphologically identical to females and juveniles, respectively (here seen on the outer sponge surface), attempt to sneak past the 2 alpha male guarding the entrance to copulate with the females within. DUFFY_Ch02.qxd 3/4/07 6:09 PM Page 30 30 conceptual background and context There are two central issues in the study of animal mating systems: (1) the source of sexual selection and (2) the intensity of sexual selection. These issues are important because the approach researchers take to explore them determines (a) the processes that are presumed to cause sexual selection, (b) the procedures that are undertaken to observe these processes, and (c) the variables that are measured in hypothesis testing. The analysis of animal mating systems, until recently, has been based on the hypothesis that sex differences in parental investment are the source of sexual selection (reviewed in Shuster and Wade 2003; see also chapters 7, 9, 12). This emphasis was crystallized by Trivers (1972), who, following discussions by Darwin (1874), Bateman (1948), and Williams (1966), proclaimed, “What governs the operation of sexual selection is the relative parental investment of the sexes in their offspring” (p. 141). Indeed, most studies of mating systems are consistent with parental investment theory (PIT). According to this view, female reproduction is limited by the availability of resources required for parental investment, and because these resources vary in their abundance in space and in time, male reproduction is limited by the spatial distribution of resources and by the temporal distribution of sexually receptive females.To estimate the degree to which these latter distributions influence the inten- sity of selection, Emlen and Oring (1977) defined two measures: the operational sex ratio (OSR) and the environmental potential for polygamy (EPP). The OSR was originally defined by Emlen (1976, p. 283) as “the ratio of potentially receptive males to receptive females at any time.” There have been multiple interpretations of this description, but in its simplest form, OSR ϭ ϭ Ro N4/N5, where N4 and N5 equal the number of males and females, respectively (Shuster and Wade 2003).With OSR Ͼ 1, females are rare and competition for mates is presumed to be intense, although this assumption depends on the degree to which male mating success or failure is consistent among males throughout the breeding season. With OSR Ͻ 1, females are abundant and competition for mates is presum- ably relaxed, although again, depending on the cause of a female-biased sex ratio, such conditions may still allow certain males to contribute disproportionately to the next generation (Shuster and Wade 2003). The EPP measures the degree to which social and ecological conditions allow males to monopolize females. However, appropriate methods for quantifying female distributions, and the scale on which EPP should be measured were never defined. As a result, while serving as a conceptual proxy for the intensity of sexual selection, the uncertain relationship between EPP and selection intensity makes comparisons within and among species imprecise (Shuster and Wade 2003). Researchers emphasizing PIT have encountered further difficulties in putting its assumptions to rigorous empirical tests. Despite Trivers’s (1972) prediction, a sex difference in relative parental investment has proven extremely difficult to compare within and among species. Not only are the relative amounts of energy, cost, and risk associated with relative parental investment difficult to quantify (Strohm and Linsenmair 1999; see also chapters 7–9), but also, the correlation between sex differ- ences in parental investment and sexual dimorphism is dismal, particularly in species with sex role reversal (S.M. Shuster and M.J. Wade, unpublished data). Measures of sexual selection intensity based on PIT require laboratory conditions that are rarely encountered in nature (e.g., potential reproductive rate; Clutton-Brock and Vincent 1991) or make assumptions that underestimate the variance in mating success among DUFFY_Ch02.qxd 3/4/07 6:09 PM Page 31 the evolution of crustacean mating systems 31 individuals (e.g., Q, which focuses on individuals “qualified” to mate; Ahnesjö et al. 2001). Moreover, like other research paradigms grounded in optimality theory (reviewed in Cheverud and Moore 1998), PIT has an unfortunate tendency to empha- size adaptive outcomes, wherein researchers declare to what “should” evolve due to sex differences in parental investment or in expected fitness returns, and then proceed to look for evidence of adaptations consistent with their initial predictions. In this chapter, I explain the utility of a quantitative approach for measuring the source and intensity of sexual selection (see also Shuster and Wade 2003). Using ecological, life history, and behavioral data that are commonly available for sexual species, here, using crustaceans as examples, I show how the magnitude of the sex difference in fitness variance, estimated using measurements of actual male and female fitness, can be used to classify mating systems. I also show how the sex difference in fitness variance is influenced, by the spatial and temporal crowding of receptive females, by female life history, by male and female reproductive behavior, and by runaway processes in various forms. My goal is to suggest an empirical framework for the study of sexual species that measures the selective forces responsible for sex differences in adult phenotype. The Sex Difference in Fitness Variance Most research on sexual selection and its effects on mating systems, including that of Darwin (1874) himself, has focused either on the context in which sexual selection occurs (i.e., via male combat or female choice) or on the evolutionary outcome of sexual selection (i.e., on descriptions of sexual dimorphism or mating behavior). These approaches, while interesting in their own right, consider neither the process nor the degree to which sexual selection may achieve its evolutionary effects. Shuster and Wade (2003) asked, “How can sexual selection be strong enough to counter the combined, opposing forces of male and female viability selection?” (p. 10). This Quantitative Paradox is resolved by measuring the fitness variance for males and females within and among species. This method illustrates when and why sexual selection can be strong enough to overwhelm the effects of natural selection and therefore how it produces the phenotypes its researchers find so compelling. Consider a hypothetical crustacean population consisting of 20 individuals. If each of the 10 females in the population produces a clutch of 10 ova, and if each clutch is fertilized by a single male, then the total number of offspring produced ϭ ϫ ϭ is Nototal (10 ova) (10 females) 100. Because each mating pair produces 10 offspring, the total offspring produced by all females, No5, equals the total offspring ϭ produced by all males, No4 100. Because there are 10 females and 10 males in our ϭ population, the average number of offspring per female, O5 Nototal/N5 is 10, which ϭ equals the average number of offspring per male, O4 Nototal/N4. Also, because each individual produces the same number of offspring (10), no variance in offspring ϭ ϭ numbers exists for either sex. Thus, Vo5 Vo4 0. Separately calculating the mean and variance in offspring numbers for each sex shows how differences in mate numbers between the sexes may influence these parameters. Now consider a case in which 1 of the 10 males secures more than one mate (e.g., 3) as might occur in harpacticoid copepods (Stancyk and Moreira 1988) or in DUFFY_Ch02.qxd 3/4/07 6:09 PM Page 32 32 conceptual background and context cypridinid ostracods (Morin and Cohen 1991). The total offspring produced by our ϭ ϭ ϭ population, Nototal 100, remains unchanged. Similarly, because N4 N5 10, the ϭ ϭ average offspring number per male, O4 Nototal/N4 10, equals the average offspring ϭ ϭ number per female, O5 Nototal/N5 10. Because each female still secures one mate with whom she produces a single brood, the variance in offspring numbers for females, Vo5, is 0. However, because one male has three mates, two males must be excluded from mating. That is, for every k mates obtained by one male, there must be k—1 males who are unable to mate. When this happens, the variance in offspring numbers among males, Vo4, must increase. How can we quantify this increase in fitness variance among males? If paternity data are available, we could simply calculate the statistical variance in offspring numbers for males (Shuster and Wade 1991). Unfortunately, such data can be difficult to obtain (see chapter 9). An alternative approach is to partition the variance in offspring numbers within and among the classes of mating and nonmating males. The data necessary to do this, the mean and variance in mate numbers for males, and the mean and variance in offspring numbers for females, are often available in standard life history analyses. Why should we do this? This approach allows us to measure the fitness variance within each sex, which is proportional to the intensity of selection. Measures of fitness variance provide direct estimates of selection intensity, and the sex difference in selection intensity estimates the degree to which the sexes will diverge in phenotype. We begin by identifying the classes of mating males and their population ϭ frequencies. There are three such classes: males who do not mate, po ( 2/10 ϭ ϭ ϭ males 0.2), males who mate once, p1 ( 7/10 males 0.7), and males who mate ϭ ϭ three times, p3 ( 1/10 males 0.1).